1. **State the problem:** Simplify the expression $$\frac{2}{x^2 + 4x + 4} + \frac{1}{x + 2}$$. 2. **Factor the quadratic:** Notice that $$x^2 + 4x + 4$$ is a perfect square trinomial. $$x^2 + 4x + 4 = (x + 2)^2$$ 3. **Rewrite the expression:** $$\frac{2}{(x + 2)^2} + \frac{1}{x + 2}$$ 4. **Find a common denominator:** The common denominator is $$(x + 2)^2$$. Rewrite the second fraction: $$\frac{1}{x + 2} = \frac{1 \cdot (x + 2)}{(x + 2) \cdot (x + 2)} = \frac{x + 2}{(x + 2)^2}$$ 5. **Add the fractions:** $$\frac{2}{(x + 2)^2} + \frac{x + 2}{(x + 2)^2} = \frac{2 + (x + 2)}{(x + 2)^2}$$ 6. **Simplify the numerator:** $$2 + (x + 2) = x + 4$$ 7. **Final simplified expression:** $$\frac{x + 4}{(x + 2)^2}$$ This is the simplified form of the original expression. **Answer:** $$\frac{x + 4}{(x + 2)^2}$$